Factorial Calculator

Calculate the factorial of a number (n!)

Number (n)

How to Calculate Factorials

Enter a Number

Input any non-negative integer (0-170) to calculate its factorial.

Click Calculate

The calculator multiplies all integers from 1 to your number.

View Result & Steps

See the factorial value and the multiplication steps showing the calculation.

Why Use This Factorial Calculator?

✓Handle Large Numbers

Calculate factorials up to 170! using BigInt for precise results beyond standard number limits.

✓Step-by-Step Display

See the full multiplication sequence to understand how factorials are computed.

✓Zero and One Support

Correctly handles special cases where 0! = 1 and 1! = 1 by definition.

✓Input Validation

Validates input to ensure non-negative integers within calculable range.

✓Educational Tool

Perfect for learning combinatorics, probability, and discrete mathematics.

Factorial Formula & Examples

n! = n × (n-1) × (n-2) × ... × 2 × 1

Special Cases:

• 0! = 1 (by definition)
• 1! = 1
• n! = n × (n-1)! for n > 1

Example Calculations:

• 5! = 5×4×3×2×1 = 120
• 6! = 720
• 10! = 3,628,800
• 20! ≈ 2.43 × 10¹⁸

Frequently Asked Questions About Factorials

What is a factorial?

A factorial (denoted n!) is the product of all positive integers from 1 to n. For example, 5! = 5×4×3×2×1 = 120.

Why is 0! equal to 1?

Zero factorial equals 1 by mathematical convention. This definition ensures formulas like permutations and combinations work correctly for edge cases.

Where are factorials used?

Factorials are essential in combinatorics (permutations, combinations), probability theory, series expansions, and algorithm analysis.

Can factorials be calculated for negative numbers?

No, factorials are only defined for non-negative integers. Negative factorials are undefined in standard mathematics.

How fast do factorials grow?

Factorials grow extremely fast - faster than exponential. 10! is 3.6 million, 20! is 2.4 quintillion, and 170! is the largest calculable in standard systems.

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